R/sphere.R

In schloerke/geozoo: Zoo of Geometric Objects

## Sphere
#' @keywords internal
l2norm <- function(x) {
  sqrt(sum(x ^ 2))
}
#' @keywords internal
l2norm_vec <- function(x) {
  x / sqrt(sum(x ^ 2))
}

#' Sphere
#'
#' A function to generate a sphere with points on the surface
#'
#' @param p dimension of object
#' @param n number of points
#' @return
#'  \item{points }{location of points}
#'  \item{edges }{edges of the object (null)}
#' @references \url{http://schloerke.github.io/geozoo/sphere/}
#' @author Barret Schloerke
#' @examples
#' ## Generates a sphere with points on the surface
#' sphere.hollow(p = 3, n = 1000)
#'
#' @keywords dynamic
#' @export
sphere.hollow <- function(p = 3, n = p * 500) {
  tmp <- matrix(rnorm(n * p), ncol = p)
  vert <- t(apply(tmp, 1, l2norm_vec))
  wires <- NULL
  structure(
    list(points = vert, edges = wires),
    class = c("geozooNoScale", "geozoo")
  )
}


#' Solid Sphere with Equidistant Points
#'
#' A function to generate a solid sphere with equidistant points.
#'
#' @param p dimension of object
#' @param n maximum number of points in the diameter
#' @return
#'  \item{points }{location of points}
#'  \item{edges }{edges of the object (null)}
#' @references \url{http://schloerke.github.io/geozoo/sphere/}
#' @author Barret Schloerke
#' @examples
#' ## Generates a solid sphere with equidistant points
#' sphere.solid.grid(p = 3, n = 8)
#'
#' @keywords dynamic
#' @export
sphere.solid.grid <- function(p = 3, n = 8){
  cube_solid_grid <- do.call(expand.grid, rep(list(c( (0:n) / n)), p))
  cube_solid_grid <- as.matrix(cube_solid_grid)

  cube_solid_grid <- cube_solid_grid - .5
  sphere <- NULL

  for (i in 1:nrow(cube_solid_grid)) {
    tmp <- cube_solid_grid[i, ]
    if (l2norm(tmp) <= (1 / 2)){
      sphere <- rbind(sphere, tmp)
    }
  }
  vert <- sphere
  wires <- NULL
  structure(
    list(points = vert, edges = wires),
    class = c("geozooNoScale", "geozoo")
  )

}

#' Solid sphere with Random Points
#'
#' A function to generate a solid sphere with random points
#'
#' @param p dimension of object
#' @param n number of points
#' @return
#'  \item{points }{location of points}
#'  \item{edges }{edges of the object (null)}
#' @references \url{http://schloerke.github.io/geozoo/sphere/}
#' @author Barret Schloerke
#' @examples
#' ## Generates a solid sphere with random points.
#' sphere.solid.random(p = 3, n = 1000)
#'
#' @keywords dynamic
#' @export
sphere.solid.random <- function(p = 3, n = p * 500) {
  sphere <- sphere.hollow(p, n)$points
  vert <- sphere * runif(n) ^ (1 / p)
  wires <- NULL
  structure(
    list(points = vert, edges = wires),
    class = c("geozooNoScale", "geozoo")
  )

}